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Green's function Monte Carlo calculations of few nucleon systems

Brian Pudliner

Published Jan 1, 1996• 1 citation
OpenAlex

Abstract

Recently, a realistic nucleon-nucleon potential has been developed with the goal of accurately reproducing isospin symmetry breaking effects in the nuclear interaction. We briefly discuss the motivation for this potential, called Argonne $v\sb{18},$ as well as the Urbana models of three-nucleon interactions. Our approach for modeling the ground states of nuclear systems begins with the development of a variational wave function. We discuss the basis for our variational wave functions and the Monte Carlo techniques used to evaluate expectation values with these wave functions. To determine the exact ground state, Green's function Monte Carlo (GFMC) techniques are used. We review the method of GFMC in general and then discuss its application to the problem of nuclear ground states in some detail.

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Recently, a realistic nucleon-nucleon potential has been developed with the goal of accurately reproducing isospin symmetry breaking effects in the nuclear interaction. We briefly discuss the motivation for this potential, called Argonne v\sb18,v\sb{18},v\sb18, as well as the Urbana models of three-nucleon interactions. Our approach for modeling the ground states of nuclear systems begins with the development of a variational wave function. We discuss the basis for our variational wave functions and the Monte Carlo techniques used to evaluate expectation values with these wave functions. To determine the exact ground state, Green's function Monte Carlo (GFMC) techniques are used. We review the method of GFMC in general and then discuss its application to the problem of nuclear ground states in some detail.
The Green’s function Monte Carlo method used for obtaining exact solutions to the Schrödinger equation of boson systems is generalized to treat systems of several fermions. We show that when it is possible to select eigenfunctions of the Hamiltonian based on physical symmetries, the GFMC method can be used to yield the lowest energy state of that symmetry. In particular, the lowest totally antisymmetric eigenfunction, the fermion ground state, can be obtained. Calculations on several two- and three-body model problems show the method to be computationally feasible for few-body systems.
Uniform neutron matter is approximated by a cubical box containing a finite number of neutrons, with periodic boundary conditions. We report variational and Green's function Monte Carlo calculations of the ground state of fourteen neutrons in a periodic box using the Argonne ${v8}^{\ensuremath{'}}$ two-nucleon interaction at densities up to one and half times the nuclear matter density. The effects of the finite box size are estimated using variational wave functions together with cluster expansion and chain summation techniques. They are small at subnuclear densities. We discuss the expansion of the energy of low-density neutron gas in powers of its Fermi momentum. This expansion is strongly modified by the large nn\mathrm{nn}nn scattering length, and does not begin with the Fermi-gas kinetic energy, as assumed in both Skyrme and relativistic mean field theories. The leading term of neutron gas energy is approximately half the Fermi-gas kinetic energy. The quantum Monte Carlo results are also used to calibrate the accuracy of variational calculations employing Fermi hypernetted and single operator chain summation methods to study nucleon matter over a larger density range, with more realistic Hamiltonians including three-nucleon interactions.
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